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"Central Symmetry" Rotation PPT Courseware 4
1. Review questions:
1. What is axial symmetry?
If a figure folded along a certain straight line can completely coincide with another figure, then the two figures are said to be symmetrical or axially symmetric about this straight line.
2. What are the properties of two figures that are symmetric about an axis?
1. The two figures are congruent shapes.
2. The axis of symmetry is the perpendicular bisector of the line connecting the symmetry points.
3. Rotation of graphics:
In a plane, a figure is rotated by a certain angle around a fixed point. Such a figure transformation is called the rotation of the figure. The fixed point is called the rotation center, and the angle of rotation is called the rotation angle.
4. The nature of the rotation of graphics:
①. The graphics before and after rotation are congruent.
②. The distance between the corresponding point and the center of rotation is equal.
③. The angle between the corresponding point and the line segment connecting the center of rotation is equal to the angle of rotation.
5. Drawing of graphic rotation:
First connect, then create angles, and finally intercept.
research observation
(1) Rotate one of the patterns 180° around point O. What did you find?
(2) Line segments AC and BD intersect at point O, OA=OC, OB=OD. Rotate △OCD 180° around point O. What do you find?
1. Definition of central symmetry:
Rotate a figure 180 degrees around a certain point like this. If it can coincide with another figure, then we say that the two figures are symmetrical or centrally symmetrical about this point. This point is called the center of symmetry. These two figures The corresponding point in is called the symmetry point about the center.
Observation: What is the positional relationship between points C, A, and E? What is the relationship between the sizes of line segments AC and AE?
Three points C, A, and E are on a straight line or ∠CAE= 180°.AC=AE
Generalization: Properties of Centrosymmetry
(1) For two figures that are symmetric about the center, the line segments connected to the symmetry points all pass through the center of symmetry and are bisected by the center of symmetry.
(2) Two figures that are symmetric about the center are congruent shapes.
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